Introduction to Adaptive Signal Processing

Overview

ABOUT THE COURSE:Adaptive filters play a very significant role in most of today’s signal processing, communication and control applications. Their ability to process data under conditions not predictable a priori make them very useful in a diverse array of applications like radar, sonar, wireless communications, speech and audio processing, instrumentation, exploration geophysics etc. The topic of adaptive filters is very closely related to neural networks and machine learning. While a full course on adaptive filters is very involved and needs concepts from linear algebra, probability and random variables, for this particular treatment, care has been taken to maintain a minimum prerequisite requirement. Mathematical concepts necessary will be developed as part of the course. The main purpose will be to provide the participants an introduction to the subject and to prepare them for taking further studies in this and related subjects.INTENDED AUDIENCE: Students belonging to the following disciplines : Electrical Engg., Electronics and Communication Engg., Instrumentation Engg., Information technology and Computer Science, Geophysics, StatisticsPREREQUISITES: Basics of Signals and Systems and / or Digital Signal ProcessingINDUSTRY SUPPORT: Qualcomm, Signion, LRDE (DRDO), BEL, DLRL (DRDO)

Syllabus

Week 1: Basic principle of adaptive filtering and estimation; probability, random variables, conditional and joint probability densities, statistical independence, correlation and covariance.Week 2:Complex random variables, random vectors, correlation and covariance matrices, properties of Hermitian matrices (e.g., correlation / covariance matrices), positive definite forms, multivariate Gaussian densityWeek 3:Concepts of random processes, wide sense stationary (WSS) processes and their correlation structures, power spectral density, parametric modeling of WSS processes – AR, MA and ARMA processes.Week 4:Optimal FIR filters, real and complex valued optimal filters, method of steepest descentWeek 5: Least mean square (LMS) algorithm; convergence of LMS algorithm; normalized LMS, affine projectionWeek 6:Examples of adaptive filters : channel equalization, echo cancellation, interference cancellation, line enhancement, beamforming etc.Week 7:Limitations of LMS algorithm, formulation of recursive least squares (RLS) based adaptive filters, Moore-Penrose pseudo inverse, matrix inversion lemmaWeek 8:Development of the RLS transversal adaptive filter, properties, variants of the RLS family.